B.2 Greenhouse effect

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Practice exam-style IB Physics questions for Greenhouse effect, aligned with the syllabus and grouped by topic.

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Question 1

SL • Paper 1A

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SL • Paper 1A

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The Earth--atmosphere system is in approximate dynamic equilibrium over a long time interval. What condition must be satisfied by the mean radiation intensities crossing the boundary of this system?

A.

Mean reflected intensity equals mean emitted infrared intensity.

B.

Mean outgoing infrared intensity is always less than incoming intensity.

C.

Mean incoming solar intensity equals mean outgoing intensity.

D.

Mean incoming solar intensity is zero at night.

Question 2

SL • Paper 1A

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SL • Paper 1A

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A surface scatters $42\%$ of the solar radiation incident on it. What is the albedo of the surface?

A.

$0.58$

B.

$1.42$

C.

$42$

D.

$0.42$

Question 3

SL • Paper 1A

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SL • Paper 1A

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The row that lists only main greenhouse gases is

A.

$H_2O$ , $O_2$ , $CO_2$ , $N_2$

B.

$CO_2$ , $O_2$ , $H_2O$ , $N_2$

C.

$CH_4$ , $N_2$ , $O_2$ , $N_2O$

D.

$CO_2$ , $CH_4$ , $H_2O$ , $N_2O$

Question 4

SL • Paper 1A

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SL • Paper 1A

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A large area of sea ice melts and is replaced by open ocean. What is the expected direct effect on the local absorption of solar radiation?

A.

Absorption increases because the albedo decreases.

B.

Absorption increases because the emissivity decreases.

C.

Absorption decreases because the solar constant decreases.

D.

Absorption decreases because the albedo decreases.

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Question 5

SL • Paper 1A

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SL • Paper 1A

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The solar constant at a planet is $1200\ \text{W m}^{-2}$ . The planet has albedo $0.25$ . What is the mean absorbed solar intensity over the whole surface of the planet?

A.

$900\ \text{W m}^{-2}$

B.

$1600\ \text{W m}^{-2}$

C.

$225\ \text{W m}^{-2}$

D.

$300\ \text{W m}^{-2}$

Question 6

SL • Paper 1A

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SL • Paper 1A

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A greenhouse-gas molecule absorbs an infrared photon emitted by Earth's surface. What best describes the subsequent emission of infrared radiation by the molecule?

A.

It is stored permanently in molecular energy levels.

B.

It is emitted in all directions, so some may travel back toward the surface.

C.

It is converted completely into visible light travelling downward.

D.

It is emitted only upward, so all of it escapes directly to space.

Question 7

HL • Paper 1A

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HL • Paper 1A

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A grey surface at temperature $T$ radiates $3.0\times10^2\ \text{W m}^{-2}$ . A black surface at the same temperature radiates $5.0\times10^2\ \text{W m}^{-2}$ . What is the emissivity of the grey surface?

A.

$0.20$

B.

$0.60$

C.

$1.7$

D.

$0.40$

Question 8

HL • Paper 1A

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HL • Paper 1A

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A planet orbits a star at twice Earth's distance from the Sun. The star has the same luminosity as the Sun. The solar constant at Earth is $S$ . What is the stellar radiation intensity at the planet?

A.

$4S$

B.

$\dfrac{S}{2}$

C.

$\dfrac{S}{4}$

D.

$2S$

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Question 9

SL • Paper 2

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SL • Paper 2

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The Earth-atmosphere system is modelled over a long time interval. Solar radiation enters the system and radiation also leaves the system.

State the condition for the Earth-atmosphere system to be in radiative dynamic equilibrium.

[1]

Explain what happens to the average temperature of the system if the mean incoming radiation intensity is greater than the mean outgoing radiation intensity.

[2]

Question 10

SL • Paper 2

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SL • Paper 2

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Greenhouse gases form only a small fraction of Earth's atmosphere, but they are important in the energy balance.

State two main greenhouse gases other than carbon dioxide.

[1]

Outline one natural origin and one human-created or human-enhanced origin of methane.

[2]

State why nitrogen and oxygen are not considered main greenhouse gases.

[1]

Question 11

HL • Paper 1A

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HL • Paper 1A

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A spherical airless moon has emissivity $1.0$ and albedo $0.36$ . It is in radiative equilibrium at distance where the solar constant is $S$ . The equilibrium temperature is proportional to

A.

$\left(0.36S/\sigma\right)^{1/4}$

B.

$\left(0.16S/\sigma\right)^{1/4}$

C.

$\left(0.64S/\sigma\right)^{1/4}$

D.

$\left(4S/0.64\sigma\right)^{1/4}$

Question 12

HL • Paper 1A

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HL • Paper 1A

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In a simple greenhouse model, the surface temperature $T_s$ satisfies

$(1-k)\sigma T_s^4=(1-a)\frac{S}{4}$

The albedo $a$ and solar constant $S$ remain unchanged. What happens to $T_s$ when the fraction $k$ of surface-emitted infrared radiation returned to the surface increases?

A.

$T_s$ increases because the solar constant must increase.

B.

$T_s$ increases because a smaller fraction of surface radiation escapes directly.

C.

$T_s$ decreases because the atmosphere emits less radiation downward.

D.

$T_s$ remains constant because the absorbed solar intensity is unchanged.

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Question 13

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HL • Paper 1A

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The resonance model explains infrared absorption by greenhouse gases using molecular vibrations. What additional condition is needed for a vibrational mode to absorb infrared radiation strongly?

A.

The vibration must reflect visible light efficiently.

B.

The molecule must have a temperature lower than the surface.

C.

The vibration must involve a changing electric dipole.

D.

The molecule must be the most abundant gas in the atmosphere.

Question 14

SL • Paper 2

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SL • Paper 2

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A grey surface of area $2.0\ \text{m}^2$ is at a temperature of $290\ \text{K}$ . The total power radiated by the surface is $560\ \text{W}$ .

Calculate the emissivity of the surface.

[3]

Question 15

SL • Paper 2

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SL • Paper 2

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During spring, a polar surface receives a total incident solar power of $1.8\times10^{15}\ \text{W}$ . The total scattered power from the surface is $1.2\times10^{15}\ \text{W}$ .

Calculate the albedo of the polar surface.

[2]

Explain why melting of ice or snow can produce a positive feedback on warming.

[2]

Question 16

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SL • Paper 2

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The luminosity of the Sun is $3.83\times10^{26}\ \text{W}$ . The mean Earth-Sun distance is $1.50\times10^{11}\ \text{m}$ .

Calculate the solar constant at the mean Earth-Sun distance.

[2]

Outline why the small yearly change in Earth-Sun distance is not the main cause of the seasons.

[2]

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Question 17

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A planet of radius $R$ receives radiation from its star with solar constant $S$ .

Diagram of parallel rays incident on a spherical planet, showing the projected circular area perpendicular to the rays and the full spherical surface over which intercepted energy is averaged. Labels should include incident rays, projected area and spherical surface area, without giving the final ratio.

Explain why the mean incoming intensity over the whole surface of the planet is $S/4$ before reflection is considered.

[2]

For Earth, take $S=1360\ \text{W m}^{-2}$ and albedo $a=0.30$ . Calculate the mean absorbed solar intensity.

[2]

Question 18

SL • Paper 1B

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SL • Paper 1B

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Two surfaces are heated to different temperatures. The graph shows the radiated power per unit area plotted against $T^4$ for each surface.

Radiated power per unit area vs $\text{T}^{4}$ for two grey surfaces.

Determine the emissivity of surface A.

[2]

Compare the radiation emitted per unit area by surfaces A and B at the same temperature.

[1]

Suggest why visible colour alone is not sufficient to decide which surface is the better infrared emitter.

[1]

Question 19

SL • Paper 1B

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SL • Paper 1B

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Satellite measurements of reflected solar radiation were made for different latitude bands and cloud conditions.

Latitude band	Cloud condition	Incident power / $10^{14}$ W	Reflected power / $10^{14}$ W
Near equator	Clear sky	3.0	0.30
Near equator	Cloudy	3.0	0.60
Mid-latitude	Clear sky	3.0	0.75
Mid-latitude	Cloudy	3.0	1.20
High latitude	Clear sky	3.0	1.20
High latitude	Cloudy	3.0	1.80

Calculate the albedo for the cloudy high-latitude region.

[1]

Describe two trends shown by the data.

[2]

Suggest the effect on the local energy balance if high-latitude sea ice is replaced by open ocean.

[1]

Question 20

SL • Paper 1B

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SL • Paper 1B

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The table gives approximate atmospheric concentrations of selected greenhouse gases before industrialization and at present, together with examples of human-related sources.

Greenhouse gas	Before industrialization / ppm	Present / ppm	Example human-related source(s)
Carbon dioxide	280	415	Fossil-fuel combustion; deforestation
Methane	0.72	1.92	Livestock; rice paddies; landfill
Nitrous oxide	0.27	0.33	Fertilizer use; manure management; combustion

Calculate the percentage increase in the concentration of methane shown in the table.

[2]

State one human-related origin of the increase in nitrous oxide concentration.

[1]

Outline why water vapour is often described as a feedback rather than the primary human driver of the enhanced greenhouse effect.

[1]

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Question 21

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HL • Paper 1A

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A satellite surface of area $2.0\ \text{m}^2$ and emissivity $0.80$ is at $320\ \text{K}$ . Its surroundings are at $300\ \text{K}$ . Using $P_{\text{net}}=\varepsilon A\sigma(T_h^4-T_c^4)$ , which expression gives the net radiative power loss of the surface?

A.

$0.80(2.0)\sigma(300^4-320^4)$

B.

$0.80(2.0)\sigma(320^4-300^4)$

C.

$\dfrac{\sigma(320^4-300^4)}{0.80(2.0)}$

D.

$0.80(2.0)\sigma(320-300)^4$

Question 22

HL • Paper 2

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HL • Paper 2

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An airless moon orbits a star where the solar constant at the moon is $910\ \text{W m}^{-2}$ . The moon has albedo $0.12$ and infrared emissivity $0.95$ . Assume the moon reaches radiative equilibrium and has a uniform surface temperature.

Calculate the equilibrium temperature of the moon.

[4]

Question 23

HL • Paper 2

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HL • Paper 2

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A simple model of the greenhouse effect is

$(1-k)\sigma T_{\text{s}}^4=(1-a)\frac{S}{4}$

where $k$ is the fraction of surface-emitted infrared radiation returned to the surface by the atmosphere. For Earth take $T_{\text{s}}=288\ \text{K}$ , $a=0.30$ and $S=1360\ \text{W m}^{-2}$ .

Calculate the value of $k$ in this model.

[3]

State the effect on the equilibrium surface temperature if greenhouse-gas concentration increases $k$ , with all other quantities unchanged.

[1]

Question 24

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HL • Paper 2

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The graph shows the transmittance of Earth's atmosphere for infrared radiation emitted by the surface. Several absorption bands are labelled with the main absorbing gases.

Wavelength / µm	Transmittance / %	Band label
2.7	15	$H_2O$
4.3	5	$CO_2$
6.3	10	$H_2O$
8.0	75	atmospheric window
9.6	15	$O_3$
10.5	85	atmospheric window
15.0	1	$CO_2$
18.0	30	$H_2O$

State what a low value of transmittance at a particular wavelength means for infrared radiation at that wavelength.

[1]

Explain how absorption bands due to greenhouse gases reduce the rate at which the surface cools to space.

[2]

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Question 25

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HL • Paper 2

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A region of sea ice receives a mean incident solar intensity of $220\ \text{W m}^{-2}$ during summer. Its albedo changes from $0.62$ when ice covered to $0.08$ after melting exposes ocean water.

Calculate the increase in mean absorbed solar intensity caused by the change in albedo.

[2]

Explain why cloud cover makes Earth's albedo variable and why this makes the net climate effect of clouds difficult to predict from albedo alone.

[2]

Question 26

HL • Paper 2

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HL • Paper 2

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In a simplified energy-balance model, increased greenhouse-gas concentration increases the fraction of surface infrared radiation absorbed and returned by the atmosphere.

Simple energy-flow diagram for the surface and atmosphere showing incoming solar radiation, reflected solar radiation, infrared emitted by the surface, infrared escaping to space and infrared returned downward by the atmosphere. Arrows should be labelled qualitatively, without numerical values.

State the name given to the human-caused augmentation of the greenhouse effect.

[1]

Explain, using conservation of energy, why the average surface temperature rises when more infrared radiation is returned to the surface.

[2]

Suggest one limitation of representing the atmosphere by a single returned fraction of infrared radiation.

[1]

Question 27

SL • Paper 1B

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SL • Paper 1B

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A simplified model is used to estimate the equilibrium temperature of a rocky planet with no greenhouse atmosphere. The table gives values for a planet labelled X.

Planet	Solar constant / $W\ m^{-2}$	Albedo	Emissivity
X	900	0.22	0.85
Y	1200	0.30	0.90
Z	700	0.15	0.75
W	500	0.35	0.95

State why the mean incoming solar intensity over the whole surface of the planet is less than the solar constant at the planet.

[1]

Determine the mean absorbed solar intensity for planet X.

[2]

Calculate the equilibrium temperature of planet X.

[2]

Question 28

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SL • Paper 1B

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A spacecraft measures the solar intensity at different distances from the Sun. The graph shows intensity plotted against $1/r^2$ , where $r$ is the distance from the Sun.

Solar intensity plotted against inverse square of distance.

State the relationship between solar intensity and distance from the Sun shown by the graph.

[1]

Use the graph to determine the luminosity of the Sun.

[2]

Explain why the annual variation in solar intensity due to Earth's elliptical orbit is not the main cause of the seasons.

[1]

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Question 29

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SL • Paper 1B

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The graph shows atmospheric transmittance at different wavelengths together with the approximate wavelength range of infrared radiation emitted by Earth's surface.

Line graph of atmospheric transmittance and normalized Earth IR intensity versus wavelength.

Identify one wavelength region in which radiation emitted by Earth's surface is strongly absorbed by the atmosphere.

[1]

Explain, in terms of molecular energy levels, why greenhouse gases absorb infrared radiation at particular wavelengths.

[2]

Explain how absorption and re-emission by the gases shown can increase Earth's mean surface temperature.

[2]

Question 30

HL • Paper 1B

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HL • Paper 1B

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A climate model region in the Arctic is monitored over several decades. The graph shows changes in summer sea-ice fraction, regional albedo and mean absorbed solar intensity.

Year	Summer sea-ice fraction / fraction	Regional albedo / fraction	Mean absorbed solar intensity / $\text{W m}^{-2}$
1980	0.84	0.62	68.4
1990	0.74	0.59	73.8
2000	0.66	0.55	81.0
2010	0.55	0.51	88.2
2020	0.43	0.48	93.6

Using a mean incident solar intensity of $180\ \text{W m}^{-2}$ , calculate the increase in absorbed solar intensity when the albedo changes from $0.62$ to $0.48$ .

[2]

Describe the relationship between sea-ice fraction and albedo shown by the data.

[1]

Suggest why the change shown is a positive feedback in the climate system.

[2]

Question 31

HL • Paper 1B

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HL • Paper 1B

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A simplified model links the use of different electricity-generation methods to changes in atmospheric greenhouse-gas concentration. The graph shows the modelled change in surface temperature as a function of the change in returned-infrared fraction $k$ . A table gives direct operational carbon dioxide emissions for several electricity-generation methods.

Dataset	$\Delta k$	$\Delta T$ / K	Method	$CO_2$ / g kWh $^{-1}$
Temperature	-0.050	-6.0	—	—
Temperature	-0.025	-3.0	—	—
Temperature	0.000	0.0	—	—
Temperature	0.025	3.0	—	—
Temperature	0.050	6.0	—	—
Emissions	—	—	Coal	820
Emissions	—	—	Gas	490
Emissions	—	—	Oil	650
Emissions	—	—	Wind	0
Emissions	—	—	Nuclear	0
Emissions	—	—	Hydroelectric	0
Emissions	—	—	Solar	0

Determine the gradient of the graph near $\Delta k=0$ .

[2]

Identify one electricity-generation method in the table with very low direct operational $CO_2$ emissions.

[1]

Explain the physics link between burning fossil fuels for electricity and an increase in the returned-infrared fraction $k$ .

[1]

Question 32

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HL • Paper 2

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The diagram shows two simplified vibrational modes of a carbon dioxide molecule.

Two labelled sketches of a linear carbon dioxide molecule showing a symmetric stretching mode and a bending mode. The sketches should indicate atom positions and motion arrows but should not state which mode is infrared active.

Explain, using a resonance model, why some infrared frequencies are absorbed strongly by greenhouse-gas molecules.

[2]

Suggest why the symmetric stretch of $CO_2$ absorbs infrared radiation weakly, while a bending vibration absorbs infrared radiation strongly.

[2]

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Question 33

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HL • Paper 1B

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A one-parameter model represents the atmosphere by the fraction $k$ of surface-emitted infrared radiation returned to the surface:

$(1-k)\sigma T_s^4=(1-a)\frac{S}{4}$

The graph shows equilibrium surface temperature as a function of $k$ for a planet with Earth-like values of $S$ and $a$ .

Equilibrium surface temperature for an Earth-like planet.

Determine the value of $k$ corresponding to a surface temperature of $288\ \text{K}$ , using $S=1360\ \text{W m}^{-2}$ and $a=0.30$ .

[2]

Calculate the new equilibrium surface temperature if $k$ increases to $0.43$ while $S$ and $a$ remain unchanged.

[2]

Explain why a higher value of $k$ requires a higher equilibrium surface temperature in this model.

[1]

Question 34

HL • Paper 1B

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HL • Paper 1B

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The diagram shows a simplified annual mean energy budget for the Earth-atmosphere system. Some energy transfers are between the surface and atmosphere, while others cross the boundary of the Earth-atmosphere system.

An annotated energy-flow diagram for the Earth-atmosphere system with arrows for incoming solar radiation, reflected solar radiation, outgoing infrared radiation to space, atmospheric absorption and emission, surface absorption, surface infrared emission, infrared escape through an atmospheric window and non-radiative transfer. Two numerical values should be omitted for students to determine from conservation of energy.

Determine the infrared intensity escaping directly from the surface to space through the atmospheric window.

[1]

Calculate the non-radiative transfer of energy from the surface to the atmosphere.

[2]

Explain why the diagram can represent dynamic equilibrium even though large energy transfers occur within the system.

[2]

Question 35

HL • Paper 1B

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HL • Paper 1B

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The figure compares part of Earth's infrared emission spectrum with absorption features for a greenhouse gas. A simplified molecular energy-level diagram is also shown.

Wavelength / $\mu$ m	Earth emission / a.u.	Gas absorption / a.u.	Molecular transition
8.0	0.20	0.05	—
10.0	1.00	0.10	—
12.0	0.82	0.18	—
14.0	0.60	0.65	—
15.0	0.45	1.00	allowed vibrational transition
16.0	0.35	0.80	—
18.0	0.15	0.12	—

Calculate the photon energy for radiation of wavelength $15\ \mu\text{m}$ .

[2]

Explain why this wavelength can be strongly absorbed by the molecule shown.

[1]

State one limitation of using only a classical resonance model to explain the absorption spectrum.

[1]

Question 36

SL • Paper 2

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SL • Paper 2

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A small icy moon orbits a star. The solar constant at the moon is $900\ \text{W m}^{-2}$ . The mean albedo of the moon is $0.62$ and its infrared emissivity is $0.95$ .

A diagram of a spherical moon receiving parallel rays from a star. Show the projected circular area intercepting radiation and the whole spherical surface over which emission is averaged. Label the incident solar constant $S$, reflected radiation due to albedo, and emitted infrared radiation.

The energy balance for the moon is to be estimated using a uniform-temperature model.

I.

State what is meant by the albedo of the moon.

[1]

II.

Explain why the mean incident solar intensity before reflection is $S/4$ .

[2]

Calculate the equilibrium temperature of the moon, assuming that there is no greenhouse atmosphere.

[2]

Discuss how partial melting of surface ice could change the later temperature of the moon.

[2]

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Question 37

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SL • Paper 2

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Two roof materials are tested at the same temperature of $300\ \text{K}$ . Each roof receives the same incident solar intensity. The table gives measured radiation data.

Material	Incident solar intensity / W m $^{-2}$	Reflected solar intensity / W m $^{-2}$	Emitted infrared intensity / W m $^{-2}$
X	1000	300	413
Y	1000	150	368

Use the data in the table to compare the two roof materials.

I.

Determine the albedo of material X from its reflected and incident solar intensities.

[1]

II.

Determine the infrared emissivity of material X.

[2]

Explain why albedo and emissivity are not the same physical property.

[2]

Evaluate which roof material is more suitable for reducing daytime warming of a building.

[1]

Question 38

SL • Paper 2

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SL • Paper 2

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Satellite measurements indicate that the Earth-atmosphere system has a mean positive energy imbalance of $0.80\ \text{W m}^{-2}$ over the whole surface of Earth. The radius of Earth is $6.37\times 10^6\ \text{m}$ .

An energy-flow diagram for the Earth-atmosphere system. Show incoming solar radiation, reflected solar radiation, outgoing infrared radiation, and a small labelled positive imbalance into the system. The diagram should not include numerical answers.

Consider the meaning of energy balance for the Earth-atmosphere system.

I.

State the condition for dynamic equilibrium of the Earth-atmosphere system.

[1]

II.

Explain why a positive imbalance causes warming even though the imbalance is small compared with the solar constant.

[2]

Calculate the total rate at which energy is being gained by the Earth-atmosphere system.

[2]

Explain how increased greenhouse-gas concentration can produce such an imbalance.

[3]

Question 39

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HL • Paper 1B

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A survey compares three airless moons orbiting different stars. The table gives the stellar constant at each moon, its mean albedo, its infrared emissivity and its measured mean surface temperature.

Moon	Stellar constant / W m $^{-2}$	Mean albedo	Infrared emissivity	Measured mean surface temperature / K
A	800	0.35	0.90	233
B	600	0.10	0.60	245
C	400	0.50	0.95	179

Calculate the equilibrium temperature predicted for moon B using the data in the table.

[2]

Compare the effects of high albedo and low emissivity on the equilibrium temperature of a moon.

[2]

Suggest one reason why the measured mean surface temperature of a real moon could differ from the value predicted by this simple radiative model.

[1]

Question 40

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SL • Paper 2

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The main gases in dry air are nitrogen and oxygen, but the main greenhouse gases include $H_2O$ , $CO_2$ , $CH_4$ and $N_2O$ .

A molecular-level diagram showing outgoing infrared radiation from Earth's surface interacting with trace greenhouse gas molecules in the atmosphere. Show absorption followed by re-emission in several directions, labelled "re-emitted infrared radiation" and without indicating that all radiation returns to the surface.

Consider the origin of greenhouse gases.

I.

Identify two greenhouse gases other than water vapour.

[1]

II.

For one gas identified in (a)(i), outline one natural origin and one human-enhanced origin.

[2]

Explain the absorption and re-emission of infrared radiation by greenhouse-gas molecules in terms of molecular energy levels.

[3]

Suggest why nitrogen and oxygen are not listed as main greenhouse gases.

[1]

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Question 41

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SL • Paper 2

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A planet orbits a star of luminosity $3.83\times 10^{26}\ \text{W}$ at a mean orbital radius of $2.28\times 10^{11}\ \text{m}$ . The planet has albedo $0.25$ and infrared emissivity $0.90$ .

A star at the centre of an imaginary sphere passing through the orbit of a planet. Label the star luminosity $L$, orbital radius $r$, and radiation spread over area $4\pi r^2$.

Use the inverse-square model for radiation from the star.

I.

Explain why the intensity at the planet is given by $S=L/(4\pi r^2)$ .

[2]

II.

Calculate the solar constant at the planet.

[1]

Determine the equilibrium temperature of the planet if it has no greenhouse atmosphere.

[2]

Discuss one limitation of this estimate for the real surface temperature of the planet.

[2]

Question 42

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SL • Paper 2

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In a simple greenhouse model for Earth,

$(1-k)\sigma T_s^4=(1-a)\frac{S}{4}$

where $k$ is the fraction of surface-emitted infrared radiation returned to the surface. Take $S=1360\ \text{W m}^{-2}$ , $a=0.30$ and $T_s=288\ \text{K}$ .

A simple surface-atmosphere exchange diagram. Show incoming solar radiation, reflected solar radiation, upward surface infrared radiation, and a fraction returned downward by the atmosphere labelled $k$.

Use the model to quantify the greenhouse effect.

I.

Determine the value of $k$ for the given data.

[2]

II.

Calculate the new surface temperature if $k$ increases by $0.05$ while $S$ and $a$ remain unchanged.

[2]

Explain why the burning of fossil fuels is a primary cause of the enhanced greenhouse effect.

[2]

Evaluate whether this simple model proves that the calculated temperature rise will occur exactly in the real climate system.

[2]

Question 43

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

A simplified model of a planet's atmosphere uses

$(1-k)\sigma T_s^4=(1-a)\frac{S}{4}$

where $k$ is the fraction of surface infrared radiation returned to the surface. For the planet, $S=1500\ \text{W m}^{-2}$ and $a=0.31$ . The present value of $k$ is estimated to be $0.42$ .

A planet with a single atmospheric layer. Show absorbed solar radiation at the surface-atmosphere system, infrared radiation emitted by the surface, a fraction returned downward by the atmosphere, and the remainder escaping to space.

The present value of $k$ is estimated to be $0.42$ .

I.

Determine the present surface temperature predicted by the model.

[2]

II.

An enhanced greenhouse effect increases $k$ to $0.50$ . Calculate the change in surface temperature.

[2]

Explain, using conservation of energy, why the surface temperature must rise when $k$ increases and $S$ and $a$ do not change.

[2]

Discuss two assumptions in this model that limit its use for predicting a real climate.

[2]

Question 44

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

A satellite records the transmittance of Earth's atmosphere at different infrared wavelengths. Strong absorption bands are observed near wavelengths associated with vibrations of $CO_2$ , $CH_4$ and $H_2O$ .

Representative infrared transmittance spectrum of Earth’s atmosphere.

Interpret the transmittance spectrum.

I.

State what is meant by a low transmittance at a particular infrared wavelength.

[1]

II.

Explain why absorption occurs only in particular wavelength bands.

[2]

Compare the resonance model and the molecular energy-level model for greenhouse-gas absorption.

[3]

Evaluate one limitation of using only a simple resonance model to explain the greenhouse effect.

[2]

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Question 45

HL • Paper 2

Hard

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HL • Paper 2

Hard

Calculator Permitted

Because Earth's orbit is elliptical, the solar constant is about $1410\ \text{W m}^{-2}$ at one time of year and $1320\ \text{W m}^{-2}$ about six months later. Assume for this question that albedo and emissivity remain constant.

A not-to-scale elliptical orbit of Earth around the Sun. Mark two orbital positions with different distances from the Sun and label the larger and smaller solar constants. Also indicate the tilt of Earth's rotation axis qualitatively.

Consider the effect of the changing solar constant on a simple equilibrium-temperature model.

I.

Show that, if albedo and emissivity are unchanged, the equilibrium temperature is proportional to $S^{1/4}$ .

[2]

II.

Estimate the temperature difference between the two orbital positions if the lower-solar-constant equilibrium temperature is $255\ \text{K}$ .

[1]

Explain why this variation in solar constant is not the main cause of seasons on Earth.

[2]

Discuss why the same change in solar constant does not produce an immediate uniform change in surface temperature everywhere on Earth.

[2]

Question 46

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

Calculator Permitted

Two cloud layers are considered in a climate model. Cloud layer A is thick and bright. Cloud layer B is thin and high. Both affect incoming solar radiation and outgoing infrared radiation.

Cloud layer	Description	Incoming SW / W m $^{-2}$	SW reflected / W m $^{-2}$	SW reaching surface / W m $^{-2}$	LW absorbed / W m $^{-2}$	LW returned downward / W m $^{-2}$
A	thick, bright, low	300	240	60	35	20
B	thin, high	300	60	240	120	80

Analyse the competing effects of clouds on Earth's radiation balance.

I.

Explain how a thick bright cloud can reduce surface warming during the day.

[2]

II.

Explain how a thin high cloud can increase surface warming at night.

[2]

Evaluate why the statement 'more cloud always cools Earth' is not a valid conclusion from physics.

[3]

Suggest one reason why daily variation in cloud cover causes daily variation in Earth's albedo.

[1]

Question 47

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

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An exoplanet receives a stellar constant of $1100\ \text{W m}^{-2}$ and has albedo $0.20$ . Its measured mean surface temperature is $300\ \text{K}$ . Assume the surface behaves as a black body and use the simple model

$(1-k)\sigma T_s^4=(1-a)\frac{S}{4}.$

A simplified exoplanet energy-balance diagram with incoming stellar radiation, reflected radiation, surface infrared emission, and atmospheric back radiation represented by fraction $k$.

Use the measured temperature to infer the effect of the atmosphere.

I.

Calculate the mean absorbed stellar intensity.

[1]

II.

Determine the value of $k$ required by the model.

[3]

Calculate the equilibrium temperature the exoplanet would have in the absence of a greenhouse atmosphere, keeping the same albedo.

[2]

Discuss whether a large value of $k$ alone identifies which greenhouse gas is present.

[2]

Question 48

HL • Paper 2

Hard

Calculator Permitted

HL • Paper 2

Hard

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In one Arctic summer, an area $1.2\times 10^{13}\ \text{m}^2$ of sea ice is replaced by open ocean. During the affected period the mean incident solar intensity on this region is $300\ \text{W m}^{-2}$ for $90$ days. The albedo of sea ice is $0.65$ and the albedo of open ocean is $0.10$ .

A before-and-after Arctic surface diagram. Show a high-albedo sea-ice region reflecting much incoming solar radiation and a lower-albedo open-ocean region absorbing more solar radiation. Label incident solar intensity and reflected radiation qualitatively.

Estimate the additional solar energy absorbed because of the change in surface.

I.

Calculate the increase in absorbed intensity for the changed region.

[2]

II.

Calculate the additional energy absorbed during the $90$ days.

[2]

Explain why this albedo change is described as a positive feedback in climate physics.

[2]

Evaluate one limitation of using the calculation in (a) to predict the actual temperature change of the Arctic Ocean.

[2]

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B.1 Thermal energy transfers

B.3 Gas laws

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